The Finite Element Method and Applications in Engineering Using ANSYS®

663 Pages·2015·51.054 MB·English

by  Erdogan Madenci, Ibrahim Guven (auth.)

The Finite Element Method and Applications
in Engineering Using ANSYS®
Erdogan Madenci • Ibrahim Guven
The Finite Element
Method and Applications
in Engineering Using
ANSYS®
Second Edition
Springer is a brand of Springer US
1 3
Erdogan Madenci Ibrahim Guven
Department of Aerospace and Mechanical Department of Mechanical and Nuclear
Engineering Engineering
The University of Arizona Virginia Commonwealth University
Tucson, Arizona Richmond, Virginia
USA USA
Reproduction of all Copyrighted Material of ANSYS software and GUI was with the permis-
sion of ANSYS, Inc. ANSYS, Inc. product names are trademarks or registered trademarks of
ANSYS, Inc. or its subsidiaries in the United States or other countries.
ISBN 978-1-4899-7549-2 ISBN 978-1-4899-7550-8 (eBook)
DOI 10.1007/978-1-4899-7550-8
Library of Congress Control Number: 2014955722
Springer New York Heidelberg Dordrecht London
© Springer International Publishing 2015
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of
the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recita-
tion, broadcasting, reproduction on microfilms or in any other physical way, and transmission or in-
formation storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar
methodology now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publica-
tion does not imply, even in the absence of a specific statement, that such names are exempt from the
relevant protective laws and regulations and therefore free for general use.
The publisher, the authors and the editors are safe to assume that the advice and information in this book
are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the
editors give a warranty, express or implied, with respect to the material contained herein or for any errors
or omissions that may have been made.
Printed on acid-free paper
Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The finite element method (FEM) has become a staple for predicting and simulating
the physical behavior of complex engineering systems. The commercial finite ele-
ment analysis (FEA) programs have gained common acceptance among engineers
in industry and researchers at universities and government laboratories. Therefore,
academic engineering departments include graduate or undergraduate senior-level
courses that cover not only the theory of FEM but also its applications using the
commercially available FEA programs.
The goal of this book is to provide students with a theoretical and practical
knowledge of the finite element method and the skills required to analyze engineer-
ing problems with ANSYS®, a commercially available FEA program. This book,
designed for seniors and first-year graduate students, as well as practicing engi-
neers, is introductory and self-contained in order to minimize the need for addi-
tional reference material.
In addition to the fundamental topics in finite element methods, it presents ad-
vanced topics concerning modeling and analysis with ANSYS®. These topics are
introduced through extensive examples in a step-by-step fashion from various en-
gineering disciplines. The book focuses on the use of ANSYS® through both the
Graphics User Interface (GUI) and the ANSYS® Parametric Design Language
(APDL). Furthermore, it includes a CD-ROM with the “input” files for the example
problems so that the students can regenerate them on their own computers. Because
of printing costs, the printed figures and screen shots are all in gray scale. However,
color versions are provided on the accompanying CD-ROM.
Chapter 1 provides an introduction to the concept of FEM. In Chap. 2, the analy-
sis capabilities and fundamentals of ANSYS®, as well as practical modeling con-
siderations, are presented. The fundamentals of discretization and approximation
functions are presented in Chap. 3. The modeling techniques and details of mesh
generation in ANSYS® are presented in Chap. 4. Steps for obtaining solutions and
reviews of results are presented in Chap. 5. In Chap. 6, the derivation of finite ele-
ment equations based on the method of weighted residuals and principle of mini-
mum potential energy is explained and demonstrated through example problems.
The use of commands and APDL and the development of macro files are presented
in Chap. 7. In Chap. 8, example problems on linear structural analysis are worked
v
vi Preface
out in detail in a step-by-step fashion. The example problems related to heat transfer
and moisture diffusion are demonstrated in Chap. 9. Nonlinear structural problems
are presented in Chap. 10. Advanced topics concerning submodeling, substructur-
ing, interaction with external files, and modification of ANSYS®-GUI are presented
in Chap. 11.
There are more than 40 example problems considered in this book; solutions to
most of these problems using ANSYS® are demonstrated using GUI in a step-by-
step fashion. The remaining problems are demonstrated using the APDL. However,
the steps taken in either GUI- or APDL-based solutions may not be the optimum/
shortest possible way. Considering the steps involved in obtaining solutions to en-
gineering problems (e.g., model generation, meshing, solution options, etc.), there
exist many different routes to achieve the same solution. Therefore, the authors
strongly encourage the students/engineers to experiment with modifications to the
analysis steps presented in this book.
We are greatly indebted to Connie Spencer for her invaluable efforts in typing,
editing, and assisting with each detail associated with the completion of this book.
Also, we appreciate the contributions made by Dr. Atila Barut, Dr. Erkan Oterkus,
Dr. Abigail Agwai, Dr. Manabendra Das, and Dr. Bahattin Kilic in the solution of
the example problems. Last, but not least, we thank Mr. Mehmet Dorduncu for his
careful review of the modeling steps and example problems, and for capturing the
ANSYS screen shots in this version of the book. The permission provided by AN-
SYS, Inc. to print the screen shots is also appreciated.
Contents
1 Introduction ................................................................................................ 1
1.1 Concept ............................................................................................... 1
1.2 Nodes ................................................................................................... 3
1.3 Elements .............................................................................................. 3
1.4 Direct Approach .................................................................................. 4
1.4.1 Linear Spring ........................................................................... 5
1.4.2 Heat Flow ................................................................................ 6
1.4.3 Assembly of the Global System of Equations ......................... 7
1.4.4 Solution of the Global System of Equations ........................... 11
1.4.5 Boundary Conditions .............................................................. 12
2 F undamentals of ANSYS ........................................................................... 15
2.1 Useful Definitions ............................................................................... 15
2.2 Before an ANSYS Session .................................................................. 16
2.2.1 A nalysis Discipline.................................................................. 16
2.2.2 T ime Dependence .................................................................... 17
2.2.3 Nonlinearity............................................................................. 18
2.2.4 Practical Modeling Considerations ......................................... 19
2.3 Organization of ANSYS Software ...................................................... 25
2.4 ANSYS Analysis Approach................................................................. 25
2.4.1 A NSYS Preprocessor .............................................................. 26
2.4.2 A NSYS Solution Processor ..................................................... 26
2.4.3 A NSYS General Postprocessor ............................................... 26
2.4.4 ANSYS Time History Postprocessor ...................................... 26
2.5 A NSYS File Structure ......................................................................... 26
2.5.1 Database File ........................................................................... 27
2.5.2 Log File ................................................................................... 27
2.6 Error File ............................................................................................. 27
2.6.1 Results Files ............................................................................ 28
2.7 Description of ANSYS Menus and Windows ..................................... 28
2.7.1 Utility Menu ............................................................................ 28
2.7.2 Main Menu .............................................................................. 30
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viii Contents
2.7.3 T oolbar .................................................................................... 30
2.7.4 Input Field ............................................................................... 30
2.7.5 Graphics Window .................................................................... 30
2.7.6 Output Window ....................................................................... 30
2.8 Using the ANSYS Help System .......................................................... 31
2.8.1 Help Contents .......................................................................... 31
2.8.2 Help Index ............................................................................... 32
2.8.3 Search in Help ......................................................................... 32
2.8.4 V erification Manual ................................................................. 33
3 Fundamentals of Discretization ................................................................ 35
3.1 Local and Global Numbering .............................................................. 35
3.2 A pproximation Functions .................................................................... 35
3.3 Coordinate Systems ............................................................................. 40
3.3.1 Generalized Coordinates ......................................................... 40
3.3.2 Global Coordinates.................................................................. 40
3.3.3 Local Coordinates ................................................................... 40
3.3.4 Natural Coordinates ................................................................ 41
3.4 Shape Functions .................................................................................. 47
3.4.1 Linear Line Element with Two Nodes .................................... 50
3.4.2 Quadratic Line Element with Three Nodes:
Centroidal Coordinate ............................................................. 52
3.4.3 Linear Triangular Element with Three Nodes:
Global Coordinate ................................................................... 53
3.4.4 Quadratic Triangular Element with Six Nodes ....................... 55
3.4.5 Linear Quadrilateral Element with Four Nodes:
Centroidal Coordinate ............................................................. 57
3.5 Isoparametric Elements: Curved Boundaries ...................................... 59
3.6 Numerical Evaluation of Integrals ...................................................... 63
3.6.1 Line Integrals .......................................................................... 63
3.6.2 T riangular Area Integrals ........................................................ 67
3.6.3 Quadrilateral Area Integrals .................................................... 69
3.7 Problems .............................................................................................. 72
4 ANSYS Preprocessor ................................................................................. 75
4.1 Fundamentals of Modeling ................................................................. 75
4.2 Modeling Operations ........................................................................... 75
4.2.1 T itle ........................................................................................ 76
4.2.2 Elements ................................................................................. 76
4.2.3 Real Constants ........................................................................ 82
4.2.4 Material Properties .................................................................. 84
4.2.5 Element Attributes ................................................................... 86
4.2.6 Interaction with the Graphics Window: Picking Entities ........ 87
4.2.7 Coordinate Systems ................................................................. 90
Contents ix
4.2.8 W orking Plane ....................................................................... 92
4.3 Solid Modeling .................................................................................. 95
4.3.1 Bottom-up Approach: Entities............................................... 96
4.3.2 T op-Down Approach: Primitives .......................................... 102
4.4 Boolean Operators ............................................................................. 107
4.4.1 A dding ................................................................................... 108
4.4.2 Subtracting ............................................................................ 108
4.4.3 Overlap .................................................................................. 110
4.4.4 Gluing .................................................................................... 110
4.4.5 Dividing................................................................................. 111
4.5 A dditional Operations ....................................................................... 113
4.5.1 Extrusion .............................................................................. 113
4.5.2 Moving and Copying............................................................. 117
4.5.3 Keeping/Deleting Original Entities ....................................... 119
4.5.4 Listing Entities ..................................................................... 120
4.5.5 Deleting Entities .................................................................... 120
4.6 V iewing a Model ............................................................................... 121
4.6.1 Plotting: PanZoom, and Rotate Functions ............................ 121
4.6.2 Plotting/Listing Entities ........................................................ 123
4.6.3 Numbers in the Graphics Window ........................................ 124
4.7 Meshing ............................................................................................. 125
4.7.1 A utomatic Meshing ............................................................... 125
4.7.2 Manipulation of the Mesh ..................................................... 132
4.8 Selecting and Components ................................................................ 133
4.8.1 Selecting Operations ............................................................. 133
4.8.2 Components........................................................................... 136
5 ANSYS Solution and Postprocessing ...................................................... 139
5.1 Overview ........................................................................................... 139
5.2 Solution ............................................................................................. 140
5.2.1 Analysis Options/Solution Controls ...................................... 141
5.2.2 Boundary Conditions ............................................................ 143
5.2.3 Initial Conditions ................................................................... 144
5.2.4 Body Loads ........................................................................... 144
5.2.5 Solution in Single and Multiple Load Steps ......................... 145
5.2.6 Failure to Obtain Solution ..................................................... 148
5.3 Postprocessing ................................................................................... 149
5.3.1 General Postprocessor ........................................................... 150
5.3.2 T ime History Postprocessor .................................................. 150
5.3.3 Read Results .......................................................................... 151
5.3.4 Plot Results............................................................................ 153
5.3.5 Element Tables ...................................................................... 156
5.3.6 List Results ............................................................................ 159
5.4 Example: One-dimensional Transient Heat Transfer ........................ 159
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6 Finite Element Equations ........................................................................ 177
6.1 Method of Weighted Residuals ......................................................... 177
6.1.1 Example: One-Dimensional Differential Equation
with Line Elements ............................................................... 179
6.1.2 Example: Two-Dimensional Differential Equation
with Linear Triangular Elements ........................................... 187
6.1.3 Example: Two-Dimensional Differential Equation
with Linear Quadrilateral Elements ...................................... 203
6.2 Principle of Minimum Potential Energy ........................................... 221
6.2.1 Example: One-Dimensional Analysis
with Line Elements ............................................................... 228
6.2.2 T wo-Dimensional Structural Analysis .................................. 234
6.3 Problems ............................................................................................ 272
7 Use of Commands in ANSYS .................................................................. 281
7.1 Basic ANSYS Commands ................................................................. 281
7.1.1 Operators and Functions ....................................................... 285
7.1.2 Defining Parameters .............................................................. 286
7.2 A Typical Input File ........................................................................... 290
7.3 Selecting Operations ......................................................................... 292
7.4 Extracting Information from ANSYS ............................................... 297
7.5 Programming with ANSYS ............................................................... 300
7.5.1 DO Loops .............................................................................. 300
7.5.2 IF Statements ......................................................................... 302
7.5.3 /OUTPUT and *VWRITE Commands ................................. 304
7.6 Macro Files ........................................................................................ 306
7.7 Useful Resources ............................................................................... 308
7.7.1 Using the Log File for Programming .................................... 308
7.7.2 Using the Verification Problems for Programming ............... 310
8 L inear Structural Analysis ...................................................................... 313
8.1 Static Analysis ................................................................................... 313
8.1.1 T russes ................................................................................... 313
8.1.2 Beams .................................................................................... 320
8.1.3 T hree-Dimensional Problems ................................................ 325
8.1.4 T wo-Dimensional Idealizations ............................................. 329
8.1.5 Plates and Shells .................................................................... 355
8.2 Linear Buckling Analysis .................................................................. 383
8.3 T hermomechanical Analysis ............................................................. 392
8.4 Fracture Mechanics Analysis ............................................................ 400
8.5 Dynamic Analysis ............................................................................. 411
8.5.1 Modal Analysis...................................................................... 413
8.5.2 Harmonic Analysis ................................................................ 423
8.5.3 T ransient Analysis ................................................................. 437